5x(x+54)=90

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Solution for 5x(x+54)=90 equation:



5x(x+54)=90
We move all terms to the left:
5x(x+54)-(90)=0
We multiply parentheses
5x^2+270x-90=0
a = 5; b = 270; c = -90;
Δ = b2-4ac
Δ = 2702-4·5·(-90)
Δ = 74700
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:
$\sqrt{\Delta}=\sqrt{74700}=\sqrt{900*83}=\sqrt{900}*\sqrt{83}=30\sqrt{83}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(270)-30\sqrt{83}}{2*5}=\frac{-270-30\sqrt{83}}{10} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(270)+30\sqrt{83}}{2*5}=\frac{-270+30\sqrt{83}}{10} $

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